Plastered in mud and with a broad grin, three-year-old Bobby Roberts seemed intent on disproving a report published on Friday by the National Trust which warns action is not being taken to reverse the trend of Britain's children playing less outdoors and in wild places.

Romping through daffodils where Leeds' Temple Newsam park merges into unkempt scrub and woodland, he was one of a scampering gang from a playgroup.

"He's too dirty for the urban farm, isn't he?" said his mother Rachael, whose husband has knocked rungs into their back garden tree so Bobby can learn to climb. If there's truth in the National Trust's claim that half the UK's children are banned from tree-climbing, Bobby and all his friends – even the girls – are in the other half.

Exceptions can prove rules, however, and the trust report draws on data which suggests that comfortable, sophisticated home attractions – TV, computers and electronic games – are at risk of creating a generation of what the National Trust calls "cotton wool" kids. The trend has been 'dramatic and rapid' according to the research, probably encouraged by insurance-driven health and safety measures and media-led scares about child safety.

Entitled Natural Childhood, the report draws on findings by Natural England in 2009 that fewer than 10% of children play in wild places compared with 40% of adults when they were young, and academic papers from the 1990s which suggest that children's "roaming radius" from home had shrunk by 90% in 30 years.

It also quotes data from a Play England study in 2008 which showed that three times as many children went to hospital after falling out of bed, than after falling from trees.

"Authority figures and layers of bureaucracy have combined with a climate of 'don't do that' to create an environment where fewer and fewer children play in the outdoors," it says. "This has led to a situation where children playing out can even be painted as showing signs of anti-social behaviour."

The director-general of the National Trust, Fiona Reynolds, said: "Getting outdoors and closer to nature helps to keep children fit, they can learn about the world around them, and most of all its fun. Building a den, picking flowers, climbing trees – the outdoors is a treasure trove, rich in imagination. It brings huge benefits that we believe every child should have the opportunity to experience. And there are huge costs when they don't."

The report's author Stephen Moss, a naturalist and writer, said that the problem had been recognised for some time but action was proving slow to follow. He said: "The time to act is now, whilst we still have a generation of parents and grandparents who grew up outdoors and can pass, on their experience and whilst there remains a determination to do something positive in this area. Organisations that have an interest in this area, whether working in our towns and cities or in the countryside, have to connect what they are doing and commit to a long-term approach that really makes a difference."

The trust also announced a two-month inquiry as the next stage of its Outdoor Nation campaign, aimed at encouraging modern versions of Richmal Crompton's William and his sidekick Violet Elizabeth Bott. All-too familiar with authority figures and layers of bureaucracy saying 'don't', their Outlaw Gang would have obvious appeal to the likes of Bobby Roberts and his friends at Temple Newsam.

Mothers in the playgroup were ready to give evidence to the inquiry, which will also use tweets with the hashtag #naturalchildhood and email address outdoor.nation@nationaltrust.org.uk, as well as local surveys, before a national summit after consultation closes on 25 May. One of Rachael's friends said: "I know the dangers can be real because I work at Leeds crown court and sometimes have to sit in the dock beside these people.

But it's essential for children to play out and for us to guide them, so that they know the dangers and boundaries. They love the canal, for instance, and it's good that they should learn about all the wildlife there, but also about the risks of water."

Reynolds said: "We want to move the debate on and encourage people and organisations to think about how we take practical steps to reconnect children with the natural world and inspire them to get outdoors."